Volume Calculator
Calculate the volume of cube, rectangular prism, triangular prism, cylinder, sphere, hemisphere, cone and pyramid with step-by-step formulas.
A shipping box, a water tank and a geometry exercise can use the same volume formula, but only when the solid has been identified correctly. Enter all lengths in one unit. Centimetres produce cm³, metres produce m³, and no unit conversion is applied behind the scenes.
Choose the solid before choosing its volume formula
What is volume? It is the three-dimensional space occupied by a solid, or the capacity inside a container. Flat shapes have area rather than volume. The volume calculator separates prisms from round solids so the required measurements are clear before a calculation begins.
| Solid | Formula | Inputs |
|---|---|---|
| Cube | V = a³ | Side |
| Rectangular prism | V = a × b × h | Length, width, height |
| Triangular prism | V = (a × h₁ / 2) × h₂ | Triangle base and height, prism length |
| Cylinder | V = π × r² × h | Radius, height |
| Sphere | V = (4/3) × π × r³ | Radius |
| Cone | V = π × r² × h / 3 | Radius, perpendicular height |
| Rectangular pyramid | V = a × b × h / 3 | Base sides, perpendicular height |
A prism volume calculator always starts with base area and multiplies by the solid's length or height. The volume of a rectangular prism is therefore length × width × height. A 4 × 3 × 6 cm box occupies 72 cm³. For a triangular prism, first find the triangle's area and then multiply by the prism length.
Round solids start with the radius
The quickest way to see how to calculate the volume of a cylinder is to multiply the circular base area by height: V = π × r² × h. A 5 cm radius and 10 cm height give about 785.4 cm³. The cylinder volume calculator expects radius, so a stated diameter must be halved before entry.
To learn how to calculate the volume of a sphere, use V = (4/3) × π × r³. With a 6 cm radius, sphere volume is about 904.8 cm³. A sphere volume calculator needs no height, while the hemisphere volume calculator returns exactly half of the full result. The volume of a cone also begins with πr², but the base-area-and-height product is divided by three.
Equal sides and pointed solids need different checks
The volume of a cube is a³ because all three dimensions are equal. The cube tab turns a 4 cm side into 4 × 4 × 4 = 64 cm³. The volume of a pyramid is its base area × perpendicular height / 3. Its height must meet the base at a right angle rather than follow a sloping edge. A cone follows the same one-third relationship with a circular base.
Convert the cubic answer into capacity
One cm³ equals one millilitre, so 1,000 cm³ equals one litre. A rectangular tank measuring 80 × 35 × 40 cm has a theoretical capacity of 112,000 cm³, or 112 litres. One m³ equals 1,000 litres. Wall thickness and space above the fill line reduce the usable amount.
Before any volume calculation, convert mixed lengths into one unit. Then check whether a round measurement is a radius or diameter and whether a cone or pyramid height is perpendicular. The substituted values shown in the result panel make those input errors easier to catch while learning how to calculate volume.
Frequently Asked Questions About the Volume Calculator
Use V = π × r² × h. A cylinder with a 5 cm radius and 10 cm height has a volume of about 785.4 cm³.
The formula uses radius. If you know the diameter, divide it by two before entering the value; a 12 cm diameter means a 6 cm radius.
It multiplies one side length by itself three times: V = a³. A cube with a 4 cm side occupies 64 cm³.
A cone or pyramid occupies one third of the matching cylinder or prism when the base area and perpendicular height are the same. The cone volume calculator and pyramid volume calculator apply that factor automatically.
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